Can YOLO detect large objects?
The example given based on the yolov1 paper:


The last layer has a tensor of the dimension 7x7x30. but the dimension of the last tensor is not in every case 7x7x30.

let be:
S: the number of grid cells in X and Y direction
C: the number classes to train
B: the number of bounding boxes in every grid cell

The dimension of the output tensor is calculated with this formula: SxSx(5*B+C). The given example in their paper has the following values:
S:7
B:2
C:20
(7X7X(5*2+20) = 7x7x30)

With this configuration you can detect at most 96 object (SSB -> 7*7*2) and 2 objects per grid cell. (e.g. it's not possible to detect many small object in a few grid cells)

now lets consider what are each feature map of the last tensor used for:

The data of every bounding box is stored in 5 feature maps:
- 1 Feature map for the bounding box center in x direction
- 1 Feature map for the bounding box center in y direction
- 1 Feature map for the height of the bounding box
- 1 Feature map for the width of the bounding box
- 1 Feature map for the "confidence score" of the feature map

(confidence score = P(Object)*IoU(BoundingBox,Object))


P(Object): the probability that in this cell is an object
IoU: Intersection over Union. A ration between the overlapping area and the union area:



additional there are a feature map for every class. In every cell the following probability is calculated: P(Cass|Object)

Long story short:
If the bounding box is bigger than one grid cell, then some neurons share the same values (they share the bounding box center, the bounding box size and the confidence score, because they refer to the same bounding box).

Source:
https://pjreddie.com/media/files/papers/yolo_1.pdf

edit no Bounding boxes on the image

if there are no bounding boxes on the image, then the confidence score would be zero, because there are no overlapping area. you can configure the threshold of the confidence score. look at this sample picture with threshold 0: 

additionally the feature maps of the classes would be zero because every neuron represents this probability P(Class|Object) because P(Class|Object) = P(Class And Object) / p(Object); (P(Class) = 0 -> P(Class and Object) = 0)

Is adding images without bounding boxes to the training set useful?
I think it helps to lower the number of false positive matches. But that is just a guess. I have trained yolo to detect this plant https://en.wikipedia.org/wiki/Rumex_obtusifolius and I added a lot of picture without bouding boxes, becuase a low number of false positive matches was important. The result: the specificity was >99%.  

Hope this helps